Do the graphs for an oligopoly and a monopolistically competitive market have supply curves?
Monopolies, oligopolies, and mono. competitive markets have the ability to search along their demand curves for the profit-maximizing rate of output. So any price increases are decided by them, and they would have no reason to raise the price if it was not at the profit-maximizing rate of output. So their quantity supplied doesnt rely on price. Does this mean they dont have an upward-sloping supply curve?
Answer:
You've got it!
They don't have supply curves (upward sloping or otherwise). The reason is that their production decision depends on the demand curve. It makes no sense to ask "if P = $X, how much would you supply?", since they are in control of the price.
P.S. You have a misstatement. You should say "...they would have no reason to raise price if it was at the profit-maximizing rate of output." Otherwise, they would increase or decrease output.
A monopolist's supply is determined by the demand curve it faces as well as its costs. We can frame the problem as follows: The monopolists objective is to maximize her profit, given by pi = q*P(q) - c(q), where q is her quantity supplied, P(q) is the (inverse) demand curve, and c(q) is her total cost function. We can say she sets price or quantity--since she controls the market these are equivalent. Let the control variable in this case be quantity. To solve the maximization problem we set dpi/dq = 0. dpi/dq = q*dP/dq + P(q) - dc/dq; thus, dc/dq = q*dP/dq + P(q). In other words marginal cost must equal marginal revenue. (The term P(q) accounts for the income of selling one additional item, while the term q*dP/dq, accounts for the decrease in price of all items sold as a result of the increase in quantity.)
Because the monopolist controls both price and quantity, we cannot consider how she would react in quantity to a given price or vice versa. Holding the demand and cost functions constant, there will be an explicit quantity which she will supply. So, you are right; there is no "supply curve" that can be graphed on the axes of price and quantity. There is merely a quantity and a price that she will set. We can only look at how that quantity and price will change with changing market conditions.
To make it a little more concrete, we can assume some common forms for an inverse demand curve and cost function:
Say P(q) = A - Bq and C(q) = cq.
Then dP/dq = -B and dc/dq = c.
Plugging into the result above, we have c = q*(-B) + A - Bq. Solving for q, we have q = (c - A)/2B. You can take the derivative of q with respect to any of the constants we have introduced to see how the quantity supplied would change given a change in that constant. This is as close as you will come to a "supply curve."
The math is not exactly the same for oligopolists, but the concept is the same. They have some influence over price, thus you cannot consider what quantity they will supply "given" a certain price.
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Answer:
You've got it!
They don't have supply curves (upward sloping or otherwise). The reason is that their production decision depends on the demand curve. It makes no sense to ask "if P = $X, how much would you supply?", since they are in control of the price.
P.S. You have a misstatement. You should say "...they would have no reason to raise price if it was at the profit-maximizing rate of output." Otherwise, they would increase or decrease output.
A monopolist's supply is determined by the demand curve it faces as well as its costs. We can frame the problem as follows: The monopolists objective is to maximize her profit, given by pi = q*P(q) - c(q), where q is her quantity supplied, P(q) is the (inverse) demand curve, and c(q) is her total cost function. We can say she sets price or quantity--since she controls the market these are equivalent. Let the control variable in this case be quantity. To solve the maximization problem we set dpi/dq = 0. dpi/dq = q*dP/dq + P(q) - dc/dq; thus, dc/dq = q*dP/dq + P(q). In other words marginal cost must equal marginal revenue. (The term P(q) accounts for the income of selling one additional item, while the term q*dP/dq, accounts for the decrease in price of all items sold as a result of the increase in quantity.)
Because the monopolist controls both price and quantity, we cannot consider how she would react in quantity to a given price or vice versa. Holding the demand and cost functions constant, there will be an explicit quantity which she will supply. So, you are right; there is no "supply curve" that can be graphed on the axes of price and quantity. There is merely a quantity and a price that she will set. We can only look at how that quantity and price will change with changing market conditions.
To make it a little more concrete, we can assume some common forms for an inverse demand curve and cost function:
Say P(q) = A - Bq and C(q) = cq.
Then dP/dq = -B and dc/dq = c.
Plugging into the result above, we have c = q*(-B) + A - Bq. Solving for q, we have q = (c - A)/2B. You can take the derivative of q with respect to any of the constants we have introduced to see how the quantity supplied would change given a change in that constant. This is as close as you will come to a "supply curve."
The math is not exactly the same for oligopolists, but the concept is the same. They have some influence over price, thus you cannot consider what quantity they will supply "given" a certain price.
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